Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 30000)	Who ?	When ?
9001	5^73096-17006	51092	Enzo Doria	02/2013
9002	10^51091-701	51091	Robert Price	06/2017
9003	(-lucasV(1,2,339439)-2)/(79*83)	51088	Mike Oakes	03/2017
9004	2^169706-270551	51087	Gary Barnes	08/2009
9005	(2^169696+5)/21	51083	Lelio R Paula	01/2012
9007	(1722520^8192+1)/65537	51082	Syoichiro Yamada	01/2009
9006	11^49051-8760	51082	Enzo Doria	02/2013
9008	(24737*2^169672+1)/27	51080	Lelio R Paula	05/2014
9009	2^169677+16095	51078	Lelio R Paula	05/2009
9010	2^169659-135	51073	Lelio R Paula	01/2011
9011	2^169638-113183	51067	Enzo Doria	07/2014
9012	(29*2^169622-1)/2346531185	51054	Lelio R Paula	01/2014
9013	(10^51054+17)/9	51054	Robert Price	10/2014
9014	(24737*2^169577+1)/5	51052	Lelio R Paula	05/2014
9015	11^49021-78	51051	Lelio R Paula	01/2013
9016	18^40669+61	51051	Lelio R Paula	01/2013
9017	14038^4327+4327^14038	51045	Hans Havermann	02/2016
9018	2^169555-159	51042	Lelio R Paula	01/2011
9019	91^26054-2	51041	Lelio R Paula	08/2013
9020	Phi(101775,10)/1628401	51034	Makoto Kamada	05/2015
9021	97*10^51027-3	51029	Robert Price	01/2017
9022	2^169499-2647	51025	Yves Minet	07/2014
9023	5*6^65567+7	51022	Lelio R Paula	09/2014
9024	14763^2858+2858^14763	51022	Hans Havermann	08/2015
9025	24^36966-1477	51021	Enzo Doria	03/2013
9026	(78557*2^169464+1)/160527	51014	Lelio R Paula	06/2014
9027	(34*10^51008-43)/9	51009	Ray Chandler	09/2010
9028	10^51004+128427	51005	Patrick De Geest	08/2009
9030	10^51004-113	51004	Milton L. Brown	12/2008
9029	10^51003+16951	51004	Patrick De Geest	08/2009
9031	10^51003-79601	51003	Milton L. Brown	12/2008
9032	10^51003-80831	51003	Milton L. Brown	12/2008
9033	10^51002+8877	51003	Patrick De Geest	08/2009
9035	10^51002-10541	51002	Milton L. Brown	11/2008
9034	10^51001+52051	51002	Patrick De Geest	08/2009
9036	10^51001-158687	51001	Milton L. Brown	10/2008
9037	2*10^51000+93	51001	Robert Price	07/2016
9040	(2^169416+5)/3	50999	Lelio R Paula	01/2012
9038	(49*10^50998+41)/9	50999	Robert Price	07/2015
9039	13292^6867+6867^13292	50999	Hans Havermann	02/2016
9041	(35*10^50997-71)/9	50998	Robert Price	05/2015
9042	6^65536+2*97878-1	50997	Jiahao He	05/2017
9043	29^34871-28^34871	50996	Robert Price	09/2012
9044	76^27112-75	50993	Norbert Schneider	11/2012
9045	(12451^12451+1345)/2^2/19/89/139/6977	50980	Makoto Morimoto	07/2016
9046	10736^12645-12645^10736	50971	Norbert Schneider	12/2016
9048	(1017*2^169315-1)/9715	50968	Lelio R Paula	03/2015
9047	7^60309-6^(60309+1)	50968	Robert Price	06/2016
9050	2^169267+99	50955	Lelio R Paula	07/2009
9049	5*2^169264+3	50955	Lelio R Paula	02/2014
9051	t(192517)	50950	Robert Price	08/2014
9052	10^50943+624451	50944	Robert Price	03/2015
9053	10^50943+54409	50944	Patrick De Geest	02/2016
9054	10^50943-100559	50943	Patrick De Geest	03/2016
9055	2^169206-3645	50937	Lelio R Paula	05/2009
9056	2^169196-112577	50934	Enzo Doria	06/2014
9057	20^39146-3483	50931	Enzo Doria	03/2013
9058	10^50929+16849	50930	Patrick De Geest	01/2012
9060	10^50929-51	50929	Robert Price	05/2011
9059	7^60264+48	50929	Lelio R Paula	10/2012
9061	2^169167+1299	50925	Lelio R Paula	05/2009
9062	10103^12717-100	50925	Enzo Doria	07/2012
9063	3^106721-130	50919	Lelio R Paula	07/2012
9065	18225^622+622^18225	50917	Anatoly F. Selevich	11/2006
9064	(10223*2^169138+1)/1113	50917	Lelio R Paula	05/2014
9066	7*2^169125+9	50913	Lelio R Paula	02/2014
9067	(47*2^169123+1)/29	50912	Lelio R Paula	03/2015
9068	20^39131+93	50911	Lelio R Paula	01/2013
9069	(21*27^35567-94921)/26	50910	Curtis Bright	05/2015
9070	(7*2^169124-1)/9549	50909	Lelio R Paula	01/2014
9071	(12433^12433+809)/2/3/11	50907	Makoto Morimoto	07/2016
9072	13693^5212+5212^13693	50897	Hans Havermann	02/2016
9073	7*5^72813+6	50895	Lelio R Paula	09/2014
9074	5*10^50890-81	50891	Robert Price	04/2017
9075	3^106656-12028	50888	Enzo Doria	02/2013
9076	(2^169028+3)/259	50881	Lelio R Paula	01/2012
9077	2^169000-1127	50875	Yves Minet	05/2013
9078	19^39780+16	50869	Lelio R Paula	01/2013
9079	(19*2^168960+1)/5	50863	Lelio R Paula	07/2012
9080	(-lucasV(1,2,337937)-2)/(3^2*11)	50863	Mike Oakes	02/2017
9082	11^48840+46	50862	Lelio R Paula	01/2013
9081	(5*10^50861-107)/3	50862	Robert Price	01/2017
9083	20^39087-4203	50854	Enzo Doria	03/2013
9084	(12421^12421+1339)/2^4/5/43/157	50848	Makoto Morimoto	07/2016
9085	2^168907-544447	50847	Paul Bourdelais	11/2012
9086	19312^429+429^19312	50839	Anatoly F. Selevich	12/2006
9087	5^72716-13226	50827	Enzo Doria	02/2013
9088	2^168823+1025	50821	Lelio R Paula	01/2009
9089	7*10^50818-89	50819	Robert Price	01/2017
9091	2^168811+15015*168811	50818	Henri Lifchitz	02/2005
9090	2^168813-2833	50818	Yves Minet	09/2014
9092	(12413^12413+3221)/2/89	50816	Makoto Morimoto	07/2016
9093	2^168795+5385	50813	Lelio R Paula	05/2009
9094	4*3^106483+5	50806	Lelio R Paula	03/2014
9095	13^45606+4	50803	Lelio R Paula	01/2013
9096	13^45606-38	50803	Lelio R Paula	01/2013
9097	2^168746+58905	50798	Lelio R Paula	05/2009
9098	(16*10^50795-43)/9	50796	Robert Price	02/2015
9099	gcd(V(615445),5F(123089)(F(123089)-1)+1)	50794	Serge Batalov	04/2015
9100	7*10^50789-47	50790	Robert Price	02/2017
9101	2^168717-729523	50789	Paul Bourdelais	11/2012
9102	(12409^12409+136)/5^2/13/5647/473279	50788	Makoto Morimoto	07/2016
9103	(21*2^168652-1)/215	50769	Lelio R Paula	01/2014
9104	2^168629+12909	50763	Lelio R Paula	01/2011
9105	9328^12787+12787^9328	50762	Norbert Schneider	01/2016
9106	2^168627+73113	50762	Enzo Doria	04/2016
9107	2^168623+47333	50761	Yves Minet	02/2010
9108	(12401^12401+154)/3^2/5/31/59/67/97/761/863/12143	50745	Makoto Morimoto	07/2016
9109	(lucasV(1,2,337126)+2)/(5*11)	50739	Mike Oakes	02/2017
9110	8544^12901-12901^8544	50723	Norbert Schneider	05/2017
9111	(17^41221+1)/18	50720	Paul Bourdelais	03/2010
9112	10^50711+7	50712	Jason Earls	12/2007
9113	10^50711-317969	50711	Patrick De Geest	04/2009
9114	(17^41213+3^41213)/20	50710	Robert Price	08/2013
9115	(12391^12391+58)/59/211/7823	50710	Makoto Morimoto	07/2016
9117	2^168431-159	50703	Lelio R Paula	01/2011
9116	(7*10^50702-1)/3	50703	Erik Branger	03/2014
9118	117216#-p(117216)	50700	Henri Lifchitz	03/2007
9119	(1543550^8192+1)/65537	50692	Syoichiro Yamada	06/2008
9120	(13*2^168352-1)/477	50678	Lelio R Paula	01/2014
9121	8*10^50675+39	50676	Robert Price	01/2017
9122	(lucasV(1,2,336840)+2)/(1133372360970589125621*144481)	50676	Mike Oakes	02/2017
9123	14415^3274+3274^14415	50670	Hans Havermann	05/2016
9124	(12379^12379+282)/17	50663	Makoto Morimoto	07/2016
9126	5^72480-17126	50662	Enzo Doria	02/2013
9125	(34*10^50667-7)/9/3^3/136277	50662	Makoto Morimoto	04/2016
9127	3^106143+2	50644	Mike Oakes	11/2009
9128	9178^12777-12777^9178	50633	Norbert Schneider	02/2017
9129	(2*10^50603-41)/3	50603	Robert Price	01/2017
9130	(12^46889-1)/11	50601	Paul Bourdelais	09/2008
9131	2^168068-1893	50594	Yves Minet	09/2012
9132	2^168057+8415	50591	Lelio R Paula	11/2011
9133	4*10^50579+9	50580	Robert Price	05/2015
9134	2^168019-94395	50579	Lelio R Paula	07/2011
9135	2^168019+74213	50579	Enzo Doria	04/2016
9136	3^106002+70	50576	Lelio R Paula	07/2012
9137	5*2^167970-9	50565	Lelio R Paula	02/2014
9138	(58*10^50558-13)/9	50559	Robert Price	09/2015
9139	88*10^50547+7	50549	Robert Price	11/2016
9140	2^167910-112625	50546	Enzo Doria	06/2014
9141	(1476500^8192+1)/65537	50534	Syoichiro Yamada	06/2008
9142	2^167866+11715	50533	Lelio R Paula	05/2009
9143	gcd(V(621415),5F(124283)(F(124283)+1)+1)	50528	Serge Batalov	04/2015
9144	2^167847-135	50527	Lelio R Paula	01/2011
9145	-lucasV(-1,2,335684)	50526	Mike Oakes	01/2017
9146	(-lucasV(1,2,335677)+2)/(3*226777)	50519	Mike Oakes	02/2017
9147	(12347^12347+1567)/2/3^2/5	50517	Makoto Morimoto	07/2016
9149	2^167807+75	50515	Lelio R Paula	08/2010
9148	2^167805+76277	50515	Enzo Doria	04/2016
9150	8335^12882+12882^8335	50510	Norbert Schneider	03/2016
9151	7*2^167777+9	50507	Lelio R Paula	02/2014
9152	14162^3681+3681^14162	50502	Hans Havermann	05/2016
9153	(17*10^50495-11)/3	50496	Robert Price	07/2015
9154	2^167682+85	50478	Lelio R Paula	08/2010
9155	2^167667-927427	50473	Paul Bourdelais	11/2012
9156	9737^12654+12654^9737	50470	Norbert Schneider	01/2016
9157	(9179*2^167644-1)/17	50469	Lelio R Paula	03/2015
9158	13386^5891+5891^13386	50468	Hans Havermann	05/2016
9159	(lucasV(1,2,335347)+2)/(3511302287439661)	50462	Mike Oakes	02/2017
9160	5003^13637-156	50447	Enzo Doria	07/2012
9161	6^64826-26723	50445	Enzo Doria	03/2013
9162	(3^105718+7)/32	50439	Lelio R Paula	03/2012
9163	(1436724^8192+1)/65537	50437	Syoichiro Yamada	06/2008
9164	17^40989+56	50435	Lelio R Paula	01/2013
9165	(12329^12329+1652)/421	50435	Makoto Morimoto	07/2016
9166	2*5^72153+7	50434	Lelio R Paula	09/2014
9167	(3126^14431-1)/3125	50433	Richard Fischer	03/2015
9168	8078^12907-12907^8078	50432	Norbert Schneider	05/2017
9169	39^31694+38	50428	Norbert Schneider	05/2014
9170	2^167460+2187	50411	Lelio R Paula	11/2011
9171	(12323^12323+2709)/2^4	50409	Makoto Morimoto	07/2016
9172	11^48400-7710	50404	Enzo Doria	02/2013
9173	2^167432+54615	50403	Lelio R Paula	05/2009
9174	(23*2^167430-1)/4169	50400	Lelio R Paula	01/2014
9175	68677!6-2	50395	Robert Price	07/2017
9176	19^39404+22	50389	Lelio R Paula	01/2013
9177	35^32629-7834	50382	Enzo Doria	03/2013
9178	6^64744+163	50381	Lelio R Paula	06/2012
9179	116447#+174659	50381	Nicolas PALAU	09/2016
9181	2^167353+129	50379	Lelio R Paula	05/2009
9180	20^38722-1133	50379	Enzo Doria	03/2013
9183	3^105567-16	50369	Lelio R Paula	07/2012
9182	2^167321-112849	50369	Enzo Doria	06/2014
9184	(28*10^50362-43)/3	50363	Robert Price	04/2016
9185	11421^12410-12410^11421	50357	Norbert Schneider	08/2013
9186	2^167278-2063	50356	Yves Minet	03/2013
9187	181^22300+22300^181	50347	Serge Batalov	05/2014
9188	9932^12595-12595^9932	50343	Norbert Schneider	12/2016
9189	8993^12732-12732^8993	50342	Norbert Schneider	02/2017
9190	3*5^72018-4	50339	Lelio R Paula	09/2014
9191	2^167207-112687	50335	Enzo Doria	06/2014
9192	6^64674-37	50327	Lelio R Paula	06/2012
9193	2^167177+74801	50326	Enzo Doria	04/2016
9194	13739^4600+4600^13739	50323	Hans Havermann	10/2015
9195	11508^12391+12391^11508	50320	Norbert Schneider	06/2014
9196	2^167132-2163	50312	Yves Minet	08/2013
9197	7^59527-62	50307	Lelio R Paula	06/2012
9198	(310027^9161+1)/310028	50302	Faysal YAtim	04/2008
9199	(12301^12301+74)/3^2/5^3/11/17/1151	50302	Makoto Morimoto	07/2016
9200	2^167083-112519	50297	Enzo Doria	06/2014
9201	272^20659-20659^272	50296	Norbert Schneider	09/2015
9202	25337!!-16	50290	Robert Price	06/2015
9203	9722^12611-12611^9722	50290	Norbert Schneider	12/2016
9204	(15*2^167013+1)/649	50275	Lelio R Paula	07/2012
9205	19^39315-12	50275	Lelio R Paula	01/2013
9206	5^71925-36	50274	Lelio R Paula	06/2012
9207	2^167002+2799139	50273	Enzo Doria	04/2016
9208	10957^12444-12444^10957	50270	Norbert Schneider	07/2013
9209	8*10^50253-99	50254	Robert Price	02/2017
9211	5^71894-54	50252	Lelio R Paula	06/2012
9210	(127^23887+1)/128	50252	Richard Fischer	04/2017
9212	18^40028-5	50247	Lelio R Paula	01/2013
9213	(3*2^166904+1)/1279	50241	Lelio R Paula	07/2012
9214	24^36397+23	50236	Norbert Schneider	12/2013
9215	7984*29^34345+21	50230	Curtis Bright	05/2015
9216	3^105248-13528	50217	Enzo Doria	02/2013
9217	6^64532-65	50216	Lelio R Paula	06/2012
9218	5^71834-20616	50210	Enzo Doria	03/2013
9219	(31*2^166778-1)/3651	50204	Lelio R Paula	01/2014
9220	2^166752-112397	50198	Enzo Doria	06/2014
9221	(12277^12277+1746)/17/37/151	50197	Makoto Morimoto	07/2016
9223	11^48199-930	50195	Enzo Doria	11/2012
9222	3*10^50194-7	50195	Erik Branger	11/2013
9224	9992^12549+12549^9992	50192	Norbert Schneider	10/2015
9225	2^166708+157	50185	Lelio R Paula	01/2011
9226	(1338272^8192+1)/65537	50184	Syoichiro Yamada	06/2008
9227	7*2^166685+3	50179	Lelio R Paula	02/2014
9228	7*2^166671-9	50174	Lelio R Paula	02/2014
9229	9*2^166670+7	50174	Lelio R Paula	02/2014
9230	2^166670-112541	50173	Enzo Doria	06/2014
9231	2^166657+465	50169	Lelio R Paula	11/2011
9232	17^40768-20	50163	Lelio R Paula	01/2013
9233	2^166596-78795	50151	Lelio R Paula	07/2011
9234	135^23541+134	50151	Norbert Schneider	04/2015
9235	24^36335-673	50150	Enzo Doria	03/2013
9236	(12269^12269+291)/2^8/5/7/19/41/109/10426349	50150	Makoto Morimoto	07/2016
9237	(28*10^50147-97)/3	50148	Robert Price	07/2016
9238	263^20718-20718^263	50137	Norbert Schneider	09/2015
9239	t(167020)	50133	Robert Price	01/2015
9240	(12263^12263+1442)/127/5479	50133	Makoto Morimoto	07/2016
9241	2868(2340(29023#-29527)(2340(29023#-29527)+3)+1)(2868(2340(29023#-29527)(2340*(29023#-29527)	50129	Pierre CAMI	06/2008
9242	12^46445-19	50123	Lelio R Paula	12/2012
9243	2^166501-14593	50122	Enzo Doria	04/2013
9244	(31*2^166509-1)/3684077	50120	Lelio R Paula	01/2014
9245	2^166483-169	50117	Lelio R Paula	01/2011
9246	9^52515+2*6^52515-4^52515	50113	Mike Oakes	04/2010
9247	(23*2^166487-1)/33770499	50112	Lelio R Paula	01/2014
9248	2*5^71689-9	50109	Lelio R Paula	09/2014
9249	13495^5154+5154^13495	50096	Hans Havermann	04/2016
9250	6^64369-119	50089	Lelio R Paula	06/2012

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Probable Primes Top 10000

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